I've heard some actors say that it's easier to play dead with their eyes open than closed. When closed, their eyes tend to movie beneath their eyelids.
The thing that comes to my mind instantly is Brian Blessed in “I, Claudius”. Siân Phillips has this long monolog, but the camera remains on Blessed’s face all the time. He has his eyes open, apathic, and in the middle of the monolog, just dies. Nothing actually happens, but you see he’s dead now. It’s no particular expression, but all the energy has ceased. It’s totally convincing. And Blessed has to keep his eyes open and unmoving in bright lights and close-up for what seems like minutes. Talk about body control!